First, we need to understand whether DeRossi is a transitional coach or whether he has outgrown this status. But in any case, whether he stays or they hire a coach with a big name, I doubt that Roma will be able to compete for the Champions League zone, even taking into account the fact that Serie A will most likely retain its 5 spots.
Roughly speaking, Inter, Milan, Juventus, Napoli will take 4 tickets and Lazio, Atalanta, Bologna, Roma will apply for the remaining one with equal chances - so the chances on paper are 25%.
We never know what will be going to happen in next season with things are never been easy to predict here in Serie A while it's one of the wired leagues for me in this season we are having two surprises with Bologna and Atlanta are joining top five and who could be in next season it's never been easy to predict with we are having Inter, AC Milan and Juventus could be stayed, but others have to give their best with their consistency is also important while we are having too many surprises and wired results which usually happen near the end of the season give big setbacks to many teams.
Good thing now we are having top eight teams which are having some good quality and consistency for staying into top ranks with can Napoli fight back and Bologna will be able to stay at this level it's quite interesting with Roma, Atlanta and Lazio could be in good touch always.